Subgroups — C₃²×C₄²⋊C₉ #13047786

Order 1296.

262 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄²	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄²⋊C₉	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₂²⋊C₉	—	4	1	no	maximal
4	C₂×C₃³×C₄	—	3	1	no	—
5	C₃²×C₄²	C₉	1	9	yes	complemented
6	C₃²×C₄²	C₃²	1	4	yes	—
7	C₄²⋊C₉	C₃²	1	9	yes	direct product factor
8	C₂²×C₃³	A₄	1	1	yes	characteristic
9	C₃³×C₄	—	3	2	no	—
10	C₃×C₂²⋊C₉	—	4	12	no	—
11	C₃²×C₉	—	16	1	no	Sylow
12	C₂×C₃²×C₄	—	3	9	no	—
13	C₂×C₃²×C₄	—	3	4	no	—
14	C₂×C₃³	—	3	1	no	—
15	C₃×C₄²	C₃×C₉	1	12	yes	complemented
16	C₃×C₄²	C₃³	1	1	yes	characteristic
17	C₂²×C₃²	C₂²⋊C₉	1	9	yes	—
18	C₂²×C₃²	C₃×A₄	1	4	yes	—
19	C₃²×C₄	—	3	18	no	—
20	C₃²×C₄	—	3	8	no	—
21	C₂²⋊C₉	—	4	9	no	—
22	C₃³	C₄²⋊C₃	1	1	yes	characteristic
23	C₃×C₉	—	16	12	no	—
24	C₂×C₃×C₄	—	3	12	no	—
25	C₂×C₃×C₄	—	3	1	no	—
26	C₂×C₃²	—	3	9	no	—
27	C₂×C₃²	—	3	4	no	—
28	C₄²	C₃²×C₉	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₃	C₃×C₂²⋊C₉	1	12	yes	—
30	C₂²×C₃	C₃²×A₄	1	1	yes	characteristic
31	C₃×C₄	—	3	24	no	—
32	C₃×C₄	—	3	2	no	—
33	C₃²	C₄²⋊C₉	1	9	yes	direct product factor
34	C₃²	C₃×C₄²⋊C₃	1	4	yes	—
35	C₉	—	16	9	no	—
36	C₂×C₄	—	3	1	no	—
37	C₂×C₃	—	3	12	no	—
38	C₂×C₃	—	3	1	no	—
39	C₂²	C₃²×C₂²⋊C₉	1	1	yes	characteristic
40	C₄	—	3	2	no	—
41	C₃	C₃×C₄²⋊C₉	1	12	yes	direct product factor
42	C₃	C₃²×C₄²⋊C₃	1	1	yes	characteristic
43	C₂	—	3	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.